An Experiment in Using the Internet in Teaching and Learning Mathematics

An Experiment in Using the Internet in Teaching and Learning MathematicsAuthor(s): Roger DaySource: Journal of Science Education and Technology, Vol. 7, No. 3 (Sep., 1998), pp. 249-258Published by: SpringerStable URL: http://www.jstor.org/stable/40186468 .

Accessed: 15/06/2014 07:14

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Springer is collaborating with JSTOR to digitize, preserve and extend access to Journal of Science Educationand Technology.

http://www.jstor.org

This content downloaded from 91.229.229.96 on Sun, 15 Jun 2014 07:14:01 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=springer

http://www.jstor.org/stable/40186468?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Journal of Science Education and Technology, Vol 7, No. 3, 1998

An Experiment in Using the Internet in Teaching and Learning Mathematics

Roger Day1

This article describes how the world-wide web is currently used by a mathematics educator. The author describes a multi-phase teaching experiment designed to address three questions: (1) Can the world-wide web provide students a viable way to access course materials, information, and activities? (2) What investments of time and expertise are required to deliver web-based course materials? (3) What potential is there for the Internet to positively impact upon the teaching and learning of mathematics? Illustrations of various uses of the world- wide web are provided as are comments that respond to the teaching-experiment questions. KEY WORDS: World-Wide Web; Internet; mathematics education.

INTRODUCTION

Owston (1997) cited Davies (1995) in posing three questions to ask about the impact of technology on higher education: "Does it make learning more accessible? Does it promote improved learning? Does it accomplish the above while containing, if not reducing, the per unit costs of education V (Owston, 1997, p. 27). After presenting arguments and examples in response to each of these questions from the perspective of the world-wide web, Owston concluded by noting that

a promising case exists for the web in all three areas. The case is rooted largely in how educators are ac-

tually using the web today. Many of these uses are

merely extensions of what is already being done with more established media. This is not surprising, because we tend to think of any new technology in

terms of the frame of reference with which we are most (amUiar .... No doubt further research and

development on the application of the web to teach-

ing and learning is needed. Nonetheless, in the meantime, it merits serious consideration as we search for ways to revitalize and enhance what we do in our schools. (Owston, 1997, p. 33)

This article provides a look at how one mathematics educator actually uses the world-wide web today. I describe and comment on my use of the web and other Internet resources in my work with mathematics and mathematics education students. After a brief description of my general uses of Internet tools, I describe an ongoing teaching experiment I am con- ducting. I begin by articulating three questions that have framed the experiment and describe four phases of Internet-tools applications that have evolved in my teaching activities. I include text and graphical examples to illustrate my descriptions and call on feedback from students to help substantiate my findings. I then return to the guiding questions and use them as a basis for comments and concerns emerging from the experiment.

The Experiment

I have used the Internet in my professional work since August 1993, when I began to incorporate data sets from ftp and gopher sites, and eventually from the world-wide web, into several courses, including Probability and Statistics for Middle Grades Teachers, Calculus I, Secondary Mathematics Methods, and Technology Tools for Secondary School Mathematics. Since academic year 1994-1995, students have been

'Mathematics Department, Illinois State University, Campus Box

4520, Normal, Illinois 61790-45820. e-mail: [email protected]

249 1059-0145/98A»0(M)249$15.(XM) O 1998 Plenum Publishing Corporation



250 Day

communicating with me at an increasing rate through e-mail. I have invested significant time to become familiar with world-wide web sites devoted to mathematics and mathematics education and early in 1996

began to learn HTML programming. My exposure to the web motivated me to consider its use in my teaching activities.

Phase I. I experimented with web-based course- materials dissemination during spring semester 1996 in the course Combinatorics Topics for Middle Grades Teachers. I made virtually all materials available

through the world-wide web: syllabus, lecture notes, problem sets, quizzes, tests, solutions, and grade updates. Students browsed the course homepage to read sample homework submissions in order to better understand my expectations (Fig. 1), to study course notes before and after class meetings (Fig. 2), to obtain solution keys for quizzes and tests, and to check current grade calculations.

I undertook this experiment in the combinatorics class with three questions in mind:

1. Can the world-wide web provide students a viable

way to access course materials, information, and activities? With more than one-third of the students in the course commuting to campus once a week, only for my class, there was motivation to explore alternative access.

2. What investments of my time and expertise are required to deliver web-based course materials? Suc- cess of the combinatorics course did not depend on the timely presence of web-based materials, because I maintained hard-copy versions of all course materials. Under this condition I could address the question of time and expertise requirements without the constant pressure of as- suring that high-quality electronic materials were always available to students.

3. What potential is there for the Internet to positively impact upon my teaching and learning of mathematics? This course provided a setting within which I could begin to explore the new technology.

Phase II. I extended the experiment during summer 1996 when I taught Technology Tools for Secon- dary School Mathematics. Although I did hand out some course materials, a significant portion of the course was enhanced through electronic dissemination and exchange of information that was available only in electronic form. Unlike the combinatorics course in which I simply made the paper course materials available through the web, in the summer tech-

nology course we ventured out onto the Internet to learn new information and to gather and exchange resources related to technology applications for teach-

Fig. 1. Web page providing combinatorics students with sample responses to assignments. [URL available 15 June 1998: http:/Aww.math.ilstu.edu/--day/respJevels_sarap.html]



Ail experiment in Using the Internet 251

Fig. 2. Web page providing combinatorics students with notes from class sessions. [URL available 15 June 1998:

http^/www.math.iIstiLcchi/~day/305S05Notcs.htmlJ

ing and learning mathematics. Students submitted required course assignments through e-mail and electronic file exchange and I distributed e-mail evaluations to the students (Fig. 3). During this phase of the experiment I moved from using the Internet

as a supplement to requiring its use throughout the course. The technology course was an appropriate setting for this move because a fundamental course goal was to become acquainted with technology tools appropriate for mathematics teaching and learning.

Fig. 3. Example e-mail evaluation response sent to student.



252 Day

Fig. 4. Homepage for the fall semester 1996 course Technology Tools for Secondary School Mathematics. [URL available 15 June 1998: http://www.math.ilstu.edu/~day/326F96.html]

Phase III When I taught the same technology course during fall semester 1996, 1 continued my use of the Internet. I worked to establish a more com-

prehensive course web site that provided students materials for the course as well as links to external resources (Fig. 4). In a two-part assignment, I re-

quired students to evaluate a common set of Internet resources that held potential for use in mathematics education and then to locate and evaluate another set of their choice (Fig. 5). A weekly electronic bul-

letin was available at the course web site (Fig. 6). Each bulletin provided students with reminders and highlights of course assignments as well as with links to internal and external resources. Included in each bulletin was a "Web Site of the Week" that was either an outgrowth of recent course discussions or a reflection of current events in mathematics education.

Phase IV The most recent extension to my teaching experiment has been as a supervisor of secondary

Fig. 5. Web page directing students in their review of Internet resources. [URL available 15 June 1998: http://www.math.ilstiLedu/-day/webeval.html]



An experiment in Using the Internet 253

Fig. 6. Portions of a weekly bulletin distributed in the course Technology Tools for Secondary School Mathematics Fall 1996. [URL available 15 June 1998: http://www.math.Ustu. edu/~day/32Gweekly925.html]

mathematics student teachers. During spring semester 1997, all four student teachers I supervised had Internet access. Three of them had convenient daily access while the fourth had to travel to campus to check an e-mail account and to access the Internet. With the three students that had convenient access, I modified the requirements for weekly progress re- ports so that all information exchange took place through e-mail. The three student teachers submitted required quantitative data regarding hours spent in various activities during the week and they kept me updated on changes in their school and teaching schedules. Most significantly, they wrote weekly re- flections related to their student teaching to which I could provide immediate feedback (Fig. 7).

Fig. 7. Example of student teacher reflection submitted weekly through e-mail.

Comments on My Experimental Use of Electronic Resources for Teaching and Learning Mathematics

The comments and questions that follow are based on my ongoing experiment to integrate In- ternet resources into my teaching activities. I have framed them in response to the questions I posed when I began the experiment.

L Can the World-Wide Web Provide Students a Viable Way to Access Course Materials, Information, and Activities?

Feedback from students suggests that the provi- sion of web-based course materials has been a benefit for many of them. Based on student responses to a supplement to the end-of-semester department course evaluations, 16 of 20 students in the spring semester 1996 combinatorics course had accessed the course web site on one or more occasions. Almost half of that group (7 of 16) visited the site at least once a week during the 15-week semester. Students visited the site to access a variety of materials, including grade updates (14 students), session notes

> happened that was partoiarty significant? Why made that so7 >

Wowi What a week My first 5 day week as a student teacher and was excrtng I had a tot of thtogs gong on ths week, w*h al new

ssons The student* r» th* dacses I am raschng didn't hsve any tests r quzes thtt week, so we ware toimng si weak ft was tada neat to sve myself completely r> the teacher roia for a whole week, and plan what v dass was aorta to do without onor consiitation



254 Day

(13), grading guidelines (7), problem sets (6), syllabus (4), quizzes (4), and tests (4).

Students in both the summer and fall technology courses provided written reactions to web-based de- livery of course materials (Fig. 8). Their comments show overwhelming positive support for use of the web as a way to provide access to course materials.

2 What Investments of My Time and Expertise Are Required to Deliver Web-Based Course Materials?

Despite improvements in software tools as well as the evolution of HTML standards, for many of us the learning curve for preparing materials for the web is significant. Since exposure to HTML coding in January 1996, I have invested considerable time and money to learn enough to produce useful web sites for various course activities. I have become fa-

miliar with three web-page software packages, I have used the HTML features of my word processor, and I have gained modest knowledge of HTML coding. I have learned to translate text to HTML, to convert among graphical file formats, and I know how to ftp my web pages to our department's web server. Ex- cept for creating web forms with which students submit electronic assignments or other responses, I have not yet created more interactive web sites using cgi scripts, java, and other such tools.

The symbolic and visual representations that permeate mathematics communication provide an added burden in readying materials for the web. AS- CII codes represent only a subset of the symbols we commonly use to communicate mathematics. Trans- lating word-processed symbols to images suitable for the web requires another set of skills. Visual displays, including graphs and charts, typically require format

Fig. 8. Reactions to web-based materials availability, from students in the course Technology Tools for Secondary School Mathematics.

Tough getting started but an overall time saving and effective way to disseminate information. It makes you use the computer and is cheaper than a book. The ability to view and review the course materials made completing the assignments much easier. In addition, the availability of so much additional information about additional resources was useful. I believe this method worked positively for the students. The student could never lose the syllabus or other handed out information. If the teacher needed to inform the students as a dass, he could

easily place it on the daily bulletin that the students could read any time as many times as they needed. If the student needs a hardcopy. he/she could just print it out. It let students work at a comfortable pace. I was very overwhelmed by the whole layout initially. As this made me learn about all of this

technology I see that it is a great tool in conveying this sort of information to students. The students could access the information that they needed at their convenience. I feel this method of delivering information is the best way to deliver it. Students have a quick access to see what is going on in the course. I really enjoyed this method of delivering information. It was great to have access to all the course materials in advance if you wanted. Also the links to other technology sites were interesting and

provided even more resources. The accessibility of the information for this course is wonderful. Since I hadn't had much exposure to using the internet, I would have never thought to investigate a course offered in this manner. However, this experience is a great way to share information effectively. It is a great way to get information. As a student you can reread information without feeling that

your bothering the teacher or other students. It allows for more independent learning because the teacher is available for clarifications.

> This method was okay. I really don't like reading information from the computer screen, but I am

getting more comfortable with it. It was very convenient to have a means to go back and check information.

• I think that it is an excellent way of delivering information. It is easily accessible from both home and school and can be updated in between class sessions (this was very helpful for getting last minute updates like presentation dates). It was also very helpful in securing up to date grades for the course. It also made preparing for class much easier as all the information was available in

written form on campus or from home. * I was overwhelmed by the information through the web. I am very pleased now that you did this. I

liked being able to find out what we needed to do for dass on any day or time that we chose to. > I really liked having the information online because I could check it as often as I liked. I would have

been completely lost though if I did not have access to a computer on a daily basis. Nevertheless, this was a great way to communicate about the class.

» I like this method of communication for the reason that I am able to check it at anytime from any computer. The grade updates are very helpful in knowing where I currently stand in the class.

> I felt this course had many opportunities to learn about the web. I especially like the fact that we could alwav* look in assianmants. bulletins, and nradas on the web at anvtime




translation in order to prepare web-ready materials. These are problems that many are working to eradi- cate. In the 30 months since I began applying the web to my teaching and learning activities, the proc- esses have become more streamlined.

In addition to the time and attention required to create or transform materials for the web, I also have invested considerable time to become familiar with mathematics and mathematics education resources available through the web. I have learned to use numerous web search engines and have become a regular visitor to many high-profile sites that focus on my areas of interest. I read print resources that help me learn about hardware and software advances as well as about new resources on the web. In short, I have made it a part of my professional activities to stay informed.

I am convinced that my students appreciate the flexible resource availability I have provided for them through the web. Their remarks motivate me to continue such practice. I have a bigger picture to consider, however, in making decisions about dedicating resources- my time, money, and attention, for instance-to this endeavor:

• How much time and energy are we prepared to give to such tasks? What tradeoffs must we make with other professional responsibilities and interests?

• How will such contributions be valued within our departments, colleges and universities?

• Might my students have been better off had I concentrated on other aspects of teaching and learning mathematics?

These are questions we must explore and debate. As I continue my teaching experiment, I will report additional findings.

3. What Potential Is There for the Internet to Positively Impact upon My Teaching and Learning of Mathematics?

Internet resources provide opportunities to effectively extend the teaching and learning of mathematics beyond the traditional setting wherein a group of people meet at designated times at a common physical location. Figure 9 helps situate this traditional classroom teaching and learning setting into a wider perspective that identifies potential means for electronic interactions. My applications of Internet resources in teaching and learning mathematics have thus far focused on the "different time- different location" modes of interaction. For example:

• I have used e-mail, web forms, and electronic file exchange to facilitate communication with and among students. I have provided students with e-mail feedback regarding course assignments. Students can receive and read mes- sages from various locations, including, per- haps, their place of residence. They can access their accounts any time, day or night. I can distribute comments in a much more timely manner rather than wait for class to meet again. In several instances, I have created forms that students complete and submit via the web. During the technology courses,

Fig. 9. Potential means for course participant interactions based on time and location proximity.



256

students submitted electronic versions of as-

signment responses, either handing me a disk or sending an attachment through e-mail.

• Mathematics student teachers used an electronic bulletin board, maintained by one of the student teachers, to exchange questions and comments. Again accessible at any time from many locations, student teachers and their supervisors exchanged questions, comments, and concerns and got timely feedback (Fig. 10). We used this for the first time dur-

ing spring semester 1997 student teaching and found that only a small portion of the 33 student teachers were active on the bulletin board. Those who did access the material

provided positive feedback for its continued use.

• Students refer to local and external web resources for course materials and activities. For instance, the technology course web site

provided access to problems that motivated each week's focus (Fig. 11). Students accessed those problems in advance in preparation for each week's class meeting. Each of two extended problem sets were also distributed on line, and for each problem set I established external links to web resources that were related to the problems (Fig. 12). In yet another

Day

technology course assignment, students used a course web page to launch an evaluation of five different web sites with potential for use in secondary mathematics. Students com-

pleted web forms as a way to communicate the results of their evaluations.

Students in the technology courses commented on benefits they accrued through course applications of the Internet. Among other things, their comments focused on the value of being exposed to the vast resources available through the web, the useful tech- nical lessons learned in being required to electroni-

cally transmit assignment files, and the benefit of

timely feedback to works-in-progress that helped im-

prove course projects. As is evident from my descriptions, much of my

application of the Internet to teaching and learning mathematics has revolved around extensions of what I have already been doing, a phenomenon identified

by Owston (1997). The Internet does make a wider array of resources more readily accessible, and the freedom to access those resources any time from various locations is attractive. I anticipate that as my experiment continues, I will develop more novel uses of web applications that further capitalize on the educational benefits suggested by Kearsley (1996): the web's capacity to eliminate the artificial walls

Fig. 10. Experimental web-based bulletin board used by spring semester 1997 student teachers. [URL available 15 June 1998: http^/www.heart.net/-ahackney/bbs/raath/]




Fig. 11. Technology course schedule providing access to weekly problems. [URL available 15 June 1998:

http://www.math.ilstu.ecW

classrooms and the rest of the world, the web's provi- sion of an efficient mechanism for public display of

students' work, and the web's capacity for creation and distribution of multimedia learning materials.

Fig. 12. Introduction to problem set showing hyperlinks to web resources. [URL available 15 June 1998:

hnpyAvww.math.ilstu.edu/-day/spacedebris.htrnl]



258 Day

The teaching experiment I have described here is one way I have begun to explore the potential and concerns of Internet applications for my teaching activities. The classroom journeys we make through the Internet will continue to provoke questions and provide insights into its impact upon the

teaching and learning of mathematics. I encourage us all to open the lines and share our experiences and perspectives.

REFERENCES

Davies, G. K. (1995). Higher Education's Big Problems: Can Tech- nology Help Solve Them? Keynote address at the semiannual meeting of the Eduoom National Learning Infrastructure In- itiative, Keystone, CO.

Kearsley, G. (1996). The world wide web: Global access to education. Educational Technology Review, No. 5.

Owston, R. D. (1997). The world wide web: A technology to enhance teaching and learning? Educational Researcher, 26(2): 27-33.



Documents

An Experiment in Using the Internet in Teaching and Learning Mathematics